Differential Equations

User Generated

Fgrjneg97

Mathematics

Description

A brine solution containing 3kg of salt per gallon flows at a constant rate of 20gal/minute into a tank that holds 400 gallons of pure water. The mixture in the tank is kept well stirred and flows out of the tank at the rate of 25gal/min.

a) find the mass of salt in the tank at time t

b) find the concentration of salt in the tank when there is 200 gallons of solution 

c)When will the tank be empty?

User generated content is uploaded by users for the purposes of learning and should be used following Studypool's honor code & terms of service.

Explanation & Answer

Thank you for the opportunity to help you with your question!

(a) rate in = 3kg/gal * 20gal/min = 60 kg/min

dS/dt = rate in - rate out

dS/dt = 60 - (25S)/(400-5t)

ln(S) = 60t + 5Sln(t-80) + constant

S = e^(60t + 5ln(t-80))

(b) V=200 at t = 40 minutes, so C = 10kg/gal

(c) you lose 5 gal/min, so you will be empty after 400/5 = 80 minutes = 1 hour and 20 minutes

Please let me know if you need any clarification. I'm always happy to answer your questions.


Anonymous
Really helped me to better understand my coursework. Super recommended.

Studypool
4.7
Trustpilot
4.5
Sitejabber
4.4

Related Tags